calculus step by step
Worksheet, Differentiation Calculus

Solves differentiation of a single block... $x^2, 3x^2, sin(3x)$

# calculusstep by stepcalculator

MathCrave calculus step by step solver is an advanced tool designed to efficiently solve the differential coefficient of single terms, excluding those involving summation or subtraction.
How calculus calculator works

### enter calculus expression

Enter your differential expression using the correct format

### Check sample expressions for help

Check below to see the correct way of entering a single term of differential coefficient

### result

Watch the result display on entering the expression

• 10

• 10x

• -10

• -10x

• x^(1/2)

• x^-(1/2)

• 4x^-(1/2)

• 5x^(1/2)

• -25x^(1/2)

• e^x

• e^3x

• -e^x

• -e^-x

• -e^-(5x)

• e^-(5x)

• e^(25x)

• 4e^5x

• 6e^(1/2x)

• -12e^(1/2x)

• -2e^-(1/2x)

• Inx

• In9x

• 8Inx

• 12In4x

• -12Inx

• -14In8x

• sin(x)

• cos(x)

• tan(x)

• 2sin(x)

• 4sin(3x)

• -12cos(9x)

### Inside the MathCrave Calculus Step By Step Math Solver's Brain

To find the differential coefficient of each given function, the math solver uses the basic rules of differentiation

#### Example 1:  y =12x^3

• The power rule states that if we have a function of the form y = ax^n, then its derivative is given by

• dy/dx = anx^(n-1).

• Using this rule, we can find the derivative of y =12x^3 as follows:

• dy/dx =3 *12x^(3-1)

• dy/dx = 36x^2

The differential coefficient of y =12x^3 is dy/dx =36x^2

#### Example 2:  y =4e^(3x)

The derivative of the exponential function e^x is itself, so we can differentiate

• y =4e^(3x) as follows:

• dy/dx =4 * d/dx(e^(3x))

• dy/dx =4 *3e^(3x)

• dy/dx =12e^(3x)

Therefore, the differential coefficient of y =4e^(3x) is dy/dx =12e^(3x)

#### Example 3:  y = In(4x)

The derivative of the natural logarithm function ln(x) is 1/x,

so we can differentiate y = ln (4x) as follows:

• dy/dx = d/dx(ln(4x))

• dy/dx =1/(4x) * d/dx(4x)

• dy/dx =1/(4x) *4

• dy/dx =1/x

Therefore, the differential coefficient of y = ln(4x) is dy/dx =1/x

#### Example 4: y = sin (5x)

The derivative of the sine function sin(x) is the cosine function cos(x). Using the chain rule, we can differentiate

y = sin(5x) as follows:

• dy/dx = d/dx(sin(5x))

• dy/dx = cos(5x) * d/dx(5x)

• dy/dx =5cos(5x)

The differential coefficient of y = sin(5x) is dy/dx =5cos(5x).

In summary:

• The differential coefficient of y =12x^3 is dy/dx =36x^2

• The differential coefficient of y =4e^(3x) is dy/dx =12e^(3x).

• The differential coefficient of y = ln(4x) is dy/dx =1/x

• The differential coefficient of y = sin(5x) is dy/dx =5cos(5x).

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